Curvature Distribution Research Articles

Design of rose thorn biomimetic micro-protrusion for metals and CFRTP easily disassembled joining

This study focuses on the joining techniques for metals and carbon fiber reinforced thermoplastic (CFRTP) to address the pursuit of lightweight vehicles and high recycling efficiency. The innovative concept of ‘easy-disassembly joining’ is introduced for the first time, aiming for robust joint strength and efficient disassembly/recycling of end-of-life vehicles. Inspired by rose thorn morphology and natural performances, bionic micro-protrusions are explored as intermediate structures to facilitate the easy disassembly joining between metals and CFRTP. The primary focus of the study revolves around the design strategy of micro-protrusions inspired by rose thorns. The objective is to identify the most effective micro-protrusion shapes by understanding the interplay of its geometrical parameters, including base shape, apex position, profile curvature, and stress distribution under diverse loads. Utilizing static stress numerical simulations, the study conclusively identifies an elliptical base shape with the apex positioned slightly above the right edge of the structure. The outer profile adopts a circular arc, and the inner profile follows a conical curve. This configuration effectively mitigates stress concentration at the bottom, which interfaces with the metal substrate and the smaller areas around the apex. This research introduces an innovative concept for metal-CFRTP joining and applies bionic principles in engineering solutions. By promoting lightweight and sustainable structures through enhanced disassembly efficiency, it contributes to groundbreaking advancements in the field.

Enhanced mesoscale and macroscale parameters for accurate 3D shape characterization

This paper investigates the limitations of widely used 3D Wadell's roundness and true sphericity metrics for characterizing granular materials. It introduces two improved indices: the mesoscale interlocking index and the radial distance factor. The study involves diverse particles scanned using optical interferometry and X-ray computed tomography. A mean curvature method is employed for surface segmentation, and a computationally efficient 3D mesh simplification procedure is proposed. Python scripts are developed for surface segmentation, mesh simplification, and 3D shape characterization. The new indices are validated by assessing angular and rounded 3D particles and changes in the shape of aggregates through the Los Angeles abrasion test. The results demonstrate the ability of the proposed indices to differentiate visually similar particles with identical Wadell's roundness and true sphericity, showcasing their effectiveness in accurately describing particle shape. The statistical distribution of 3D particle curvatures offers an alternative method for understanding particles' shape and abrasion.

Plastic hinge behavior of rectangular CFRP-confined RC columns: Meso-scale modelling and formulation

The ultimate rotation capacity, depending on the plastic hinge length, is a vital factor in the seismic design of flexural members. This paper focuses on the investigation of the plastic hinge length and size effect of rectangular carbon fiber-reinforced polymer (CFRP)-confined reinforced concrete (RC) columns. Firstly, considerable scatter and evident bias of the calculation results were found after evaluating existing models for calculating the plastic hinge length of FRP-confined RC columns. Accordingly, a meso-scale numerical approach was developed, with concrete heterogeneity considered, to investigate the influences of the confinement ratio and corner radius on the plastic hinge length and size effect of rectangular CFRP-confined RC columns. Results show that columns having different cross-sectional sizes exhibit similar failure patterns, and the region of lateral crack propagation for columns with lower confinement ratios is larger than that for columns with higher confinement ratios. The actual plastic hinge length is determined based on the yielding zone of reinforcement, the crushing zone of concrete, and the localization zone of curvature, while the localization zone of curvature is employed to determine the real plastic hinge zone. The size effect is found to exist in the plastic hinge length ratio, and it is weakened with the increase of the corner radius, which can be attributed to the fact that columns with higher corner ratios have more effective confinement. Taking into account the size effect, a new model for calculating the ultimate drift ratio of CFRP-confined RC columns was proposed based on an assumption of curvature distribution and presented accurate predictions.

Index for Quantifying ‘Order’ in Three-Dimensional Shapes

In this study, we focused on assessing the symmetry of shapes and quantifying an index of ‘order’ in three-dimensional shapes using curvature, which is important in product design. Specifically, the target three-dimensional shape was divided into two segments, and the Jensen–Shannon distance was calculated for the distribution of the Casorati curvatures in both segments to determine the similarity between them. This was proposed as an indicator of the ‘order’ exhibited by the shape. To validate the effectiveness of the proposed index, sensory evaluation experiments were conducted on three shapes: extruded, rotated, and vase. For the rotated shape, the coefficient of determination between the proposed index and the sensory evaluation value of ‘order’ on a 5-point Likert scale was found to be less than 0.1. The reason for the poor correlation coefficient of determination may be attributed to the bias in human perception, where individuals tend to perceive mirror symmetry with respect to the plane that includes the vertical axis when recognizing the mirror symmetry of an object. In contrast, for the extruded and vase shapes, the coefficients of determination were 0.36 and 0.66, respectively, supporting the validity of the proposed index. Nonetheless, the coefficient of determination decreased slightly for familiar extruded shapes and asymmetric vase shapes. In future research, our aim is to quantify ‘aesthetic preference’ by combining the ‘order’ and ‘complexity’ indexes.

Extraction of geometric features and analysis of flow mechanism of high loaded compressor airfoils at low Reynolds number

When the aircraft cruising at high altitude, the aerodynamic performance of the compressor sharply decreases due to the enhanced boundary layer separation loss. Therefore, it is of great significance to design the high-performance airfoils suitable for low Reynolds numbers (Re) to improve the aerodynamic performance of compressor. In this paper, numerical simulations were carried out on a high-loaded subsonic compressor cascade V103 at low Re. Meanwhile, a multi-objective optimization of blade profile was performed to get optimal solutions, and data mining techniques were applied to extract valuable design knowledge from the optimal database. The results show that the Pareto-optimal airfoils achieve a maximum reduction of 27.32% in total pressure loss coefficient under design condition and 36.71% under near stall condition. Compared with the original airfoil, the curvature distribution law of the camber line with larger values at both ends and smaller values in the middle is advantageous for the performance of the compressor cascade under design condition. This distribution pattern causes a forward shift for the loading distribution of airfoils, accompanied by an earlier transition onset. Additionally, it reduces adverse pressure gradient at the rear part of suction surface, which suppresses the development and growth of laminar separation bubble and delays the separation of turbulent boundary layer. Under near stall condition, maintaining larger leading edge angle and uniform flow diffusion is beneficial for improving the performance of compressor cascade. This is because the larger leading edge angle reduces incidence angle, while the uniform flow diffusion inhibits a great flow separation.

Pneumatically tunable adherence of elastomeric soft hollow pillars with non-circular contacts

Dynamically tunable interfacial dry adhesion plays a significant role in numerous biological functions and industrial applications. Among various strategies, pneumatics-activated adhesive devices draw much attention due to their distinct advantages such as fast speed, reliable performance, large adhesion tunability and easily accessible materials. To understand and predict adhesion strength of pneumatics-activated adhesives, it is necessary to examine their interfacial mechanics that is nonlinearly coupled with the large deformation of the devices under pressure. However, previous studies have only focused on axisymmetric cases in which the outline of the contact area is circular, whereas the tunable adherence of non-circular contact controlled by pneumatics remains elusive. In this work, through a combination of experiments and simulations, we study the effect of non-circular contact geometry on tunable dry adhesion of pressure-activated soft hollow pillars. Specifically, elliptical, square, and rectangular contact shapes are considered and their effects on tunable adhesion of the soft hollow pillars are compared to that of circular contact geometry thoroughly. The results show that soft hollow pillars with elliptical, square, and rectangular contact surfaces demonstrate rich interfacial delamination behaviors that depend on the contact outline geometry and internal pressure. Among all contact geometries, elliptical contact has the highest adhesion tunability yet requires lowest activating pressure owing to the non-uniform curvature distribution of the contact outline. However, when the eccentricity increases, the elliptical contact has reduced tunability of adhesion caused by the contact of opposing sides of the sidewall upon buckling. For square and rectangular contacts, they have the lowest adhesion tunability and need higher activating pressure than those of circular and elliptical contact since the 90-degree edges of the sidewall prohibit buckling instability. Our findings greatly broaden the design space of pneumatics-activated adhesive devices by adding the contact geometry of the soft hollow pillars as a new design parameter, which can provide valuable guidance for tunable adhesive design for various applications in manufacturing and robotics.

Debris and Smear Layer Removal in Curved Root Canals: A Comparative Study of Ultrasonic and Sonic Irrigant Activation Techniques.

The aim of this study was to compare the cleaning efficacy of three irrigant activation devices with a control of non-activated syringe and needle irrigation in curved root canals. Sixty human curved roots were endodontically prepared and divided into four groups (n = 15) with similar root curvature distributions. Final irrigation using 4% NaOCl was performed with a syringe and needle (30-G) alone, or with Eddy sonic powered irrigation system (polymeric tip #0.25/0.06), Endosonic ultrasonic activation (polymeric tip #0.25/0.03), or Irrisafe ultrasonic activation (stainless-steel tip, #0.25/0.00). SEM was used to evaluate cleaning efficacy, employing five-score systems for debris and smear layer. While no significant difference in debris removal was observed between Endosonic or Irrisafe activation and non-activated irrigation, Eddy sonic powered irrigation system significantly improved debris removal in the apical third of curved root canals. Smear layer removal was effective in coronal and mid-root sections for all groups but less so in the apical third. Thus, Eddy sonic powered irrigation system demonstrated higher efficacy in removing debris from the apical third of curved root canals compared with non-activated syringe and needle irrigation. However, all three irrigant activation systems exhibited no difference from the non-activated control in smear layer removal.

Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy.

Research efforts have been dedicated to predicting microstructural evolution during solidification processes. The main secondary arm spacing controls the mushy zone's permeability. The aim of the current work was to build a simple sub-grid model that describes the growth and coarsening of secondary side dendrite arms. The idea was to reduce the complexity of the curvature distribution with only two adjacent side arms in concurrence. The model was built and applied to the directional solidification of Al-06wt%Cu alloy in a Bridgman experiment. The model showed its effectiveness in predicting coarsening phenomena during the solidification of Al-06wt%Cu alloy. The results showed a rapid growth of both arms at an earlier stage of solidification, followed by the remelting of the smaller arm. In addition, the results are in good agreement with an available time-dependent expression which covers the growth and coarsening. Such model can be implemented as a sub-grid model in volume average models for the prediction of the evolution of the main secondary arms spacing during macroscopic solidification processes.

Effect of aspect ratio on mechanical anisotropy of lattice structures

Triply periodic minimal surface (TPMS) lattice structures with controllable mechanical properties and porous architecture are promising candidates for lightweight and energy-absorbing applications. In parametric structural design, the research on structural geometric characteristics, such as aspect ratio (R) and surface curvature, has mainly focused on fluid and heat transfer considerations. However, their impact on multi-directional mechanical properties has yet to be thoroughly investigated. This study, combining representative volume elements (RVE) based on periodic boundary conditions and theoretical surface morphological characteristics, investigates the mechanical properties and deformation behavior of lattice structures with different aspect ratios in multiple directions. The results indicate that the aspect ratio highly influences the deformation behavior of the lattice structure in different directions. The local curvature and force state of the lattice structure can be adjusted by aspect ratio to reduce local stresses and deformations in different loading directions. Compared with the simulation results of representative volume elements, the structural stress concentration and failure position can be predicted by the Gaussian curvature distribution. In addition, the elastic modulus of the structures in the [100] and [001] directions can also be adjusted by aspect ratio. Through experimental verification in the [001] direction, the structure with an aspect ratio of 2 can greatly enhance the elastic modulus (121%∼440%), maximum stress (10%∼183%), and energy absorption (33%∼85%). The significance of this work is to improve the understanding of the influence of geometric features on the mechanical properties and deformation behavior of lattice structures, which provides a new design approach for triply periodic minimal surface lattice structures in applications of impact protection and bone scaffold.

Curvature distribution, relative presentations and hyperbolicity with an application to Fibonacci groups

Given a finite presentation for a group G which can also be realised as a relative presentation we give conditions on the relative presentation which, if satisfied, proves G hyperbolic. Using a curvature distribution method we confirm these conditions for the length four one-relator relative presentation 〈u,t|tn,tmutu−r〉 for many values of r and n deduce that the corresponding generalised Fibonacci groups F(r,n) are hyperbolic.

Gaussian random field-based characterization and reconstruction of cancellous bone microstructure considering the constraint of correlation structure

The macro scale physical properties of cancellous bone materials are governed by the microstructural features, which is of great significance for the multi-scale research of cancellous bone and the inverse design of bone-mimicking materials. Therefore, it is essential to characterize the natural cancellous bone samples, and reconstruct the microstructures with the biomimetic osteointegration and mechanical properties. In this research, a novel approach for the characterization and reconstruction of cancellous bone was proposed, based on the medical image analysis and anisotropic three-dimensional Gaussian random field (GRF). The geometric similarity, i.e. the interface curvature distribution (ISD), was meticulously studied, which is important to the osteointegration ability. And the mechanical properties were validated by the stress-strain curves under the large compressive strain simulated by the smoothed particle hydrodynamic (SPH) method. In addition, the effects of the generation parameters of GRF-based biomimetic microstructures on the apparent properties were analyzed. The ISD results demonstrated that both GRF and micro-CT groups had the similar columnar morphological properties, while the latter had more hyperbolic features. And it was found that the GRF-based biomimetic microstructures and the natural bone samples based on micro-CT (MCT) had the similar failure mode. The concordance correlation coefficient between MCT and GRF pairs was 0.8685, with a Pearson ρ value of 0.8804, and significance level p<0.0001. The Bland-Altman LoA was 0.1647 MPa with 95 % (1.96SD) lower and upper bound value between −0.2892 and 0.6185 MPa. The two groups had almost the same elastic modulus with the mean absolute percentage error (MAPE) of 7.84 %. While the yield stress and total conversion energy of the GRF-based samples were lower than those of the natural bone samples, and the MAPE were 16.99 % and 16.27 %, respectively. Although it meant the lower structural efficiency, the huge design space of this approach and advanced 3D printing technology can provide great potential for the design of orthopedic implants.

Unconventional Piezoelectricity of Two-Dimensional Materials Driven by the Hall Effect.

Piezoelectricity has been widely explored for nanoelectromechanical applications, yet its working modes are mainly limited in polar directions. Here we discover the intrinsic electro-mechanical response in crystal materials that is transverse to the conventional polarized direction, which is named unconventional piezoelectricity. A Hall-like mechanism is proposed to interpret unconventional piezoelectricity as charge polarization driven by a built-in electric field for systems with asymmetric Berry curvature distributions. Density functional theory simulations and statistical analyses justify such a mechanism and confirm that unconventional piezoelectricity is a general property for various two-dimensional materials with spin splitting or valley splitting. An empirical formula is derived to connect the conventional and unconventional piezoelectricity. The extended understanding of the piezoelectric tensor in quantum materials opens an opportunity for applications in multidirectional energy conversion, broadband operation, and multifunctional sensing.

Natural Frequency Response of FG-CNT Coupled Curved Beams in Thermal Conditions

This study investigates the sensitivity of dynamic properties in coupled curved beams reinforced with carbon nanotubes (CNTs) to thermal variations. Temperature-dependent (TD) mechanical properties are considered for poly methyl methacrylate (PMMA) to be strengthened with single-walled CNTs (SWCNTs), employing the basic rule of mixture to define the equivalent mechanical properties of nanocomposites. The governing equations of motion are derived using a first-order shear deformation theory (FSDT) and Hamilton’s principle, accounting for elastic interfaces modeled using elastic springs. A meshfree solution method based on a generalized differential quadrature (GDQ) approach is employed to discretize the eigenvalue problem and to obtain the frequency response of the structure. The proposed numerical procedure’s accuracy is verified against predictions in the literature for homogeneous structural cases under a fixed environmental temperature. The systematic investigation assesses the impact of various geometric and material properties, including curvature, boundary conditions, interfacial stiffness, and CNT distribution patterns, on the vibrational behavior.

Bubble deformation and breakup in a non-uniform electric field

In this paper, the deformation and breakup characteristics of bubbles during their growth in a mixture solution were studied with a needle-ring electrode configuration in the presence of an electric field by using high-speed photography. Four distinct bubble breakup behaviors of the dripping, cone, kink and branch regimes were achieved successfully by manipulating the electric field. By considering the applied voltage and gas flow rate, the cone structure, interface stability, departure frequency and bubble size distribution in different regimes were quantitatively discussed. It is found that the cone height, interface curvature, departure frequency and bubble size distribution are evidently associated with bubble breakup regimes. As the electric field strength increased, the bubbles stretched in the direction of the electric field and the instability of the gas–liquid interface became stronger, which eventually resulted in the bubbles fragmenting into a cluster of microbubbles. This work provides a fundamental understanding of bubble deformation and breakup mechanisms under the electric field.

Thermodiffusively unstable laminar hydrogen flame in a sufficiently large 3D computational domain – Part I: Characteristic patterns

Thermodiffusive instabilities can have a leading order effect on flame propagation for lean premixed hydrogen flames. Many simulation studies have been performed to study this effect, but almost exclusively in two-dimensional (2D) or domain sizes too small to support the characteristic large-scale features of the instability. The main purpose of this study is to quantify the differences of 3D and 2D flames using simulations on sufficiently large domains. To this end, direct numerical simulations (DNS) of thermodiffusively unstable laminar premixed hydrogen flames stabilized in 3D domains were performed. The effects of confinement on the flame dynamics are rigorously investigated by varying the domain size. The flame burning velocity shows a strong dependence on the domain size when the lateral domain width is less than 50 laminar flame thicknesses. The characteristic patterns of the thermodiffusively unstable flame are analyzed in detail, including the instantaneous flame structure, global burning velocity, flame surface area, stretch factor, curvature distribution, and the cell size. The effects of the computational setup (2D vs. 3D) on the local flame front curvature and the distributions of the thermo-chemical quantities are quantified through a conditional analysis. The formation and destruction mechanisms of the distinct cellular structures observed in the 3D domain are analyzed focusing on the interactions between the flame dynamics and the flow field, and the contributions of the production of flame surface density, kinematic restoration, and curvature dissipation are quantified. Compared with the corresponding 2D simulation, the flame surface area in the cut plane of the 3D configuration is similar, yet the burning velocity and the stretch factor are increased. The reason for this is the difference in curvature statistics in 2D and 3D. In 3D, larger extreme curvature values are obtained, leading to quantitatively different distributions of the thermo-chemical variables. For example, the peak H radical concentration in the 3D simulation is about twice higher than in the 2D simulation.Novelty and significance statementThe novelty of the present work includes the following aspects:(i) First large-scale 3D DNS of laminar lean premixed hydrogen flame on domain large enough to obtain domain-independent results.(ii) First quantitative assessment of characteristic patterns of 3D thermodiffusively unstable premixed hydrogen flames.(iii) First quantitative assessment of differences between 2D and 3D thermodiffusively unstable premixed hydrogen flames for domain-independent results.

Form-finding for free-curved reinforced concrete shell structure considering structural performance and construction formwork

A computational approach for free-curved reinforced concrete (RC) shells that simultaneously considers structural performance and associated construction strategy is proposed. First, for the rapid design and construction process, a unit–formwork construction system (UFS), which uses multiple construction methods dependent on curvature, is developed, and a mock-up test is conducted to validate its effectiveness of UFS. Although the construction time was reduced, the construction costs were confirmed to be approximately twice those of conventional methods. Furthermore, the error between the measured surface coordinates of the plywood form board (PFB) and corresponding three-dimensional (3D) data is computed, and the study confirmed that the error in construction was within half of the required level. Second, a multi-objective optimization problem is formulated to obtain a shell configuration and a suitable distribution of curvatures on the PFB by minimizing the squared normal curvatures of a PFB surface and the strain energy of the completed shell structure under distributed loads. To assess the manufacturability of PFB, the normal curvatures on the surface of the PFB, which are represented as quadrilateral meshes, are calculated. Finally, numerical examples demonstrate the efficiency of the proposed method for designing a free-curved RC shell from the perspectives of structural design and constructability.

Pulsar scintillation through thick and thin: bow shocks, bubbles, and the broader interstellar medium

ABSTRACT Observations of pulsar scintillation are among the few astrophysical probes of very small-scale (≲ au) phenomena in the interstellar medium (ISM). In particular, characterization of scintillation arcs, including their curvature and intensity distributions, can be related to interstellar turbulence and potentially overpressurized plasma in local ISM inhomogeneities, such as supernova remnants, H ii regions, and bow shocks. Here we present a survey of eight pulsars conducted at the Five-hundred-metre Aperture Spherical Telescope (FAST), revealing a diverse range of scintillation arc characteristics at high sensitivity. These observations reveal more arcs than measured previously for our sample. At least nine arcs are observed toward B1929+10 at screen distances spanning $\sim 90~{{\ \rm per\ cent}}$ of the pulsar’s 361 pc path length to the observer. Four arcs are observed toward B0355+54, with one arc yielding a screen distance as close as ∼105 au (&amp;lt;1 pc) from either the pulsar or the observer. Several pulsars show highly truncated, low-curvature arcs that may be attributable to scattering near the pulsar. The scattering screen constraints are synthesized with continuum maps of the local ISM and other well-characterized pulsar scintillation arcs, yielding a three-dimensional view of the scattering media in context.

Supersymmetric higher-derivative models in quantum cosmology

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the bosons, and first order for the fermions. Upon quantization, the algebra of fermions leads to a multi-component state, which is annihilated by the Hamiltonian and supersymmetric constraint operators. We obtain asymptotic wave functions of the oscillatory type, whose classical limit corresponds to inflationary evolution, and exact exponential wave functions. We use the latter to derive probability distributions of the initial curvature that are compatible with those obtained using the non-supersymmetric model.

Bistable hybrid symmetric laminates with a clamped-clamped boundary condition: An experimental and numerical investigation

In this work, a clamped-clamped boundary condition is considered for a family of bistable hybrid symmetric laminates in which the direction of curvature does not change during the snap-through process between the two stable configurations. The laminates were modeled using finite element analysis to predict the characteristics of stable configurations, including the distributions of curvatures and out-of-plane displacement in two directions, and then the results were validated by experiments. The snap-through behaviors of the bistable laminates under the clamped-clamped boundary condition were investigated numerically and experimentally and then compared with the preloaded laminates with the same boundary condition. The results showed that the bistable laminates require a lower snap-through load than the preloaded laminates when they have a similar maximum out-of-plane displacement. The loading position, lay-up design, and length of the clamped region were employed as variables to discover the features of snap-through behavior. It was found that the unsymmetric deformation mode was present regardless of the load position during the snap-through behavior of these bistable laminates. At last, a variable cross-section tube consisting of two bistable laminates was proposed, and the area of the cross-section could be increased by 80% after the snap-through of the two bistable laminates

Structural performance of construction and demolition waste-based geopolymer concrete columns under combined axial and lateral cyclic loading

Construction and demolition waste (CDW) has reached severe environmental and economic dimensions due to its large volume among all solid waste, highlighting the importance of local actions to manage, recycle, and reuse CDW. Ductile demountable connections are necessary to disassemble and reuse the concrete structural members and fast assembly of precast structures in seismic regions without generating waste. In this study, the seismic performance of CDW-based reinforced geopolymer concrete columns has been investigated. Six ½ scaled columns (half of which were demountable and the other half monolithic) were experimentally tested under reversed cyclic lateral displacement excursions, considering three different levels of constant axial loading to determine failure mechanisms, load–displacement responses, ductilities, energy dissipation capacities, stiffness degradation relations, and curvature distributions. The obtained test results were used to determine the performance of CDW-based geopolymer concrete columns and compare the performances of the demountable connection with the monolithic connection. The test results showed that the novel demountable connection for precast concrete frames exhibited better seismic performance in terms of maximum lateral load capacity, initial stiffness, energy dissipation capacity, and maximum curvature than their monolithic counterparts. Besides, increasing the axial compression ratio on the columns caused an increase in lateral load capacity, energy dissipation capacity, energy dissipation ratio, and initial curvature stiffness; however, it decreased the ductility. Finally, the capacity predictions of current codes, i.e., TS500 and ACI318, were conservative when compared with experimental results.